An analysis of belief propagation on the turbo decoding graph with Gaussian densities

Motivated by its success in decoding turbo codes, we provide an analysis of the belief propagation algorithm on the turbo decoding graph with Gaussian densities. In this context, we are able to show that, under certain conditions, the algorithm converges and that – somewhat surprisingly – though the density generated by belief propagation may differ significantly from the desired posterior density, the means of these two densities coincide. Since computation of posterior distributions is tractable when densities are Gaussian, use of belief propagation in such a setting may appear unwarranted. Indeed, our primary motivation for studying belief propagation in this context stems from a desire to enhance our understanding of the algorithm’s dynamics in non-Gaussian setting, and to gain insights into its excellent performance in turbo codes. Nevertheless, even when the densities are Gaussian, belief propagation may sometimes provide a more efficient alternative to traditional inference methods.